Final answer:
To determine the probabilities associated with a normally distributed monthly utility bill, the appropriate Z-scores for the values in question ($65, $81, and $100) are calculated and then the standard normal distribution table is used to find the probabilities.
Step-by-step explanation:
The question revolves around the concept of a normal distribution, where monthly utility bills in a city are normally distributed with a mean of $100 and a standard deviation of $14. To solve this problem, one would typically use a standard normal distribution table or a calculator with statistical functions.
Finding the Probability of A Monthly Utility Bill Less Than $65
To find the probability that a randomly selected utility bill is less than $65, one would calculate the Z-score, which is (X - μ) / σ, where μ is the mean, σ is the standard deviation, and X is the value in question ($65 in this case). Then, use a Z-table to find the corresponding probability.
Finding the Probability of A Monthly Utility Bill Between $81 and $100
To calculate the probability that a bill falls between $81 and $100, determine the Z-scores for both values and find the area between them in the Z-table. This will give the probability for this range.
Finding the Probability of A Monthly Utility Bill More Than $100
The probability that a bill is more than $100 can be found by calculating the Z-score for $100 and subtracting the corresponding probability from 1, since we want the area to the right of $100 in the standard normal distribution.